Assessing luminosity correlations via cluster analysis: evidence for dual tracks in the radio/X-ray domain of black hole X-ray binaries

The radio/X-ray correlation for hard and quiescent state black hole X-ray binaries is critically investigated in this paper. New observations of known sources, along with newly discovered ones (since 2003), have resulted in an increasingly large number of outliers lying well outside the scatter about the quoted best-fitting relation. Most of these outliers tend to cluster below the best-fitting line, possibly indicative of two distinct tracks which might reflect different accretion regimes within the hard state. Here, we employ and compare state of the art data clustering techniques in order to identify and characterize different data groupings within the radio/X-ray luminosity plane for 18 hard and quiescent state black hole X-ray binaries with nearly simultaneous multiwavelength coverage. Linear regression is then carried out on the clustered data to infer the parameters of a relationship of the form lr=a+beta lx through a Bayesian approach (where l denotes logarithmic luminosities). We conclude that the two-cluster model, with independent linear fits, is a significant improvement over fitting all points as a single cluster. While the upper track slope (0.63 +/- 0.03) is consistent, within the errors, with the fitted slope for the 2003 relation (0.7 +/- 0.1), the lower track slope (0.98 +/- 0.08) is not consistent with the upper track or with the widely adopted value of similar or equal to 1.4 for the neutron stars. The two luminosity tracks do not reflect systematic differences in black hole spins as estimated either from reflection- or continuum-fitting method. Additionally, there is evidence for at least two sources (H1743-322 and GRO J1655-500) jumping from the lower to the upper track as they fade towards quiescence, further indicating that black hole spin does not play any major role in defining the radio loudness of compact jets from hard black hole X-ray binaries. The results of the clustering and regression analysis are fairly insensitive to the selection of subsamples, accuracy in the distances and the treatment of upper limits. Besides introducing a further level of complexity in understanding the interplay between synchrotron and Comptonized emission from black hole X-ray binaries, the existence of two tracks in the radio/X-ray domain underscores that a high level of caution must be exercised when employing black hole luminosityluminosity relations for the purpose of estimating a third parameter, such as distance or mass.